This invention relates to an apparatus and method for producing or reproducing a complex waveform over a wide frequency range while minimizing degradation and number of discrete emitters. For example, an embodiment can include a method of using wavelet transforms filtered in the wavelet domain to produce or reproduce a complex waveform over a wide frequency range while minimizing the number of discrete transponders required. Presently, there does not exist a cheap emitter or transponder that can efficiently produce or reproduce a wave based complex waveform output such as, e.g., an acoustic complex waveforms that range from the sonic to the high ultrasonic such as outputs ranging over 10 octaves. For sonic and ultrasonic devices, efficient transducers selection can be based on both cost and power are piezoelectric devices. However a typical piezoelectric device works efficiently at only 1 to 4 octaves above or below its designed operating point at lower audio frequencies and less than 1 octave above and below its design point at the higher ultra-sonic frequencies. This concept can also be extended to Radio Frequencies (RF) and other radiated energy bands in additional embodiments.
One embodiment of the invention includes use of one or more piezoelectric devices adapted to be driven by a wavelet transform that produces coefficients that are producible by digital circuits. By combining these wavelet coefficients an original signal is reproduced. By filtering in the wavelet domain, the number of transducers required to approximate the original signal to within the desired tolerances can be reduced.
Additional features and advantages of the present invention will become apparent to those skilled in the art upon consideration of the following detailed description of the illustrative embodiment exemplifying the best mode of carrying out the invention as presently perceived.